The invention relates to an electric discharge element comprising an electron source. Conventional electric discharge elements such as, for example electron tubes do not have facilities of guiding electron beams in a localized way. Moreover, they have the limitation that their electron sources produce electron currents with a limited current density. For a number of applications it would be very interesting if electric discharge elements were available with facilities of guiding electron beams in a localized way or of supplying electron currents with a larger current density. Such applications are, for example (TV) display tubes, electron microscopes, electron beam lithography devices.